No sooner had I written about the menace of pedestrians to cyclists last month, than I had my first crash with one. Cycling down the Thames Embankment I noticed three people idly crossing the road while there was a break in the traffic. Though I was travelling quite quickly, the trio were at least 30 metres away when I saw them, giving me plenty of time to ring my bell and hope they'd hurry across to the other side.

Two of them looked up and did just that, but the third didn't react. And when her friends urged her to get a move on, she simply stopped in the middle of the road. As I tried to avoid her, she moved into my path, and both of us ended up spread out across the road.

My arm was all cut up and bleeding, and as I gathered my bag and bike out of the road, I said nothing – trying to compose myself, while waiting for the pain to subside. The lady I'd hit was in her fifties, but surprisingly, she bounced back on to her feet almost immediately, and didn't seem to have come out of the collision too badly. While her husband threw a few menacing glances at me, she apologised profusely.

As I rode off, I turned back and told her she should be more careful when she was crossing the road. And she agreed.

When I told this story to my friends, they were horrified – not out of sympathy for me, however, but out of shock that I'd mown down a middle-aged woman rather than slowing down. Reading back my words, I admit that it sounds like there was plenty of time, but it all happened very quickly. I was travelling at more than 25mph, and slamming on my brakes in time to stop would probably have sent me over the handlebars.

According to the Highway Code guidelines, cars need to allow about 20 metres to come to a stop if they're travelling at 25mph – and I'm not sure it's very different for bicycles. In fact, cyclists probably need slightly longer to avoid being thrown out of the saddle.

When I first caught sight of the jaywalkers on the embankment, there was still plenty of time for them to get out of my way – and I didn't think I'd need to stop. By the time I realised that my middle-aged friend was glued to the road, it was way too late to avoid the crash.

As I mentioned in my column a few weeks ago, incidents such as this are becoming more and more common, because pedestrians underestimate a) how fast bikes are travelling and b) how much it will hurt if they end up being run over by one. And more and more are learning the lesson the hard way.

Last weekend, my colleague Howard Jacobson wrote how he believes cyclists are malevolent – and I'm sure he'd have no sympathy for me and my grazed arm. But given pedestrians' ignorance and complacency when it comes to road safety, it's no wonder many cyclists on our roads are so angry and aggressive.